While immune memory is a central feature of the immune response of vertebrates, many fundamental questions remain largely unanswered. For example we don't really know how long memory cell populations for a given pathogen will be maintained in the absence of restimulation with that pathogen, or how the decline of memory depends on exposure to new pathogens. We would like quantitative answers to these questions, and this requires the development of mathematical models. Models need to be brought into contact with experiments. To do this one needs to develop tools to analyze experimental data (such as CFSE data) in ways which allow the models to be validated. Our long-term goal is to establish a quantitative picture of how immune memory works. Such a picture is important for the design of vaccination protocols in various situations, such as in an aging population. Specific Aim 1: We will develop tools to quantitatively describe division and death of a heterogeneous population of cells from CFSE measurements (which tells us the number of cells as well as the number of divisions they have undergone). Specific Aim 2: We will develop and validate models for the longevity of CD8+ T cell memory. There are three components to this specific aim. 1. We will experimentally validate our current model (formulated in our previous grant). 2. The model developed so far works over the time scale of a few years. We will extend the model to generate a more complete description of immunological memory over the lifespan of humans. We will do this by developing models which consider cross-reactive stimulation and replicative senescence. 3. We will consider the implications of our models for vaccination by considering the loss of memory in an ageing population, the optimal boosting strategy as well as the order of delivery of multiple childhood vaccines.